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Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 1 / 7B / b / Solution

For an orthogonal projection matrix

P = P^{†} = P^{2}

,

(x, P x) = x^{†} P^{†} P x = (P x)^{†} (P x) = ∥ P x ∥^{2} \geq 0.

Thus

P

is a positive semidefinite matrix.

Solved by gpt-5.6-sol high.

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